Q. In how many ways can 5 different flags be arranged on a pole?
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Solution
The number of arrangements of 5 different flags is 5! = 120.
Correct Answer:
A
— 120
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Q. In how many ways can 5 different items be selected from 10 items?
A.
252
B.
120
C.
200
D.
300
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Solution
The number of ways to select 5 items from 10 is C(10, 5) = 252.
Correct Answer:
A
— 252
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Q. In how many ways can 5 different objects be selected from 10 objects?
A.
252
B.
120
C.
10
D.
100
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Solution
The number of ways to select 5 objects from 10 is 10C5 = 10! / (5! * 5!) = 252.
Correct Answer:
A
— 252
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Q. In how many ways can 6 different objects be selected and arranged in a line?
A.
720
B.
600
C.
840
D.
960
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Solution
The number of arrangements of 6 different objects is 6! = 720.
Correct Answer:
A
— 720
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Q. In how many ways can 6 people be divided into 2 groups of 3?
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Solution
The number of ways to divide 6 people into 2 groups of 3 is 6! / (3! * 3! * 2!) = 20.
Correct Answer:
A
— 20
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Q. In how many ways can 7 different items be selected and arranged in a line?
A.
5040
B.
720
C.
40320
D.
10080
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Solution
The number of arrangements of 7 different items is 7! = 5040.
Correct Answer:
C
— 40320
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Q. In how many ways can 7 different objects be arranged in a circle?
A.
720
B.
5040
C.
7200
D.
600
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Solution
The number of arrangements in a circle is (n-1)! = 6! = 720.
Correct Answer:
B
— 5040
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Q. In how many ways can the letters of the word 'LEVEL' be arranged?
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Solution
The word 'LEVEL' has 5 letters with 'L' and 'E' repeating. The arrangements = 5! / (2! * 2!) = 30.
Correct Answer:
B
— 30
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Q. In the expansion of (1 + x)^10, what is the coefficient of x^5?
A.
252
B.
210
C.
120
D.
300
Show solution
Solution
The coefficient of x^5 is C(10,5) = 10! / (5!5!) = 252.
Correct Answer:
A
— 252
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x?
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Solution
The coefficient of x is C(4,1) * 2^3 * 3 = 4 * 8 * 3 = 96.
Correct Answer:
A
— 12
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Q. In the expansion of (2 + 3x)^4, what is the coefficient of x^2?
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Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
B
— 54
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^1?
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Solution
The coefficient of x^1 is C(4,1) * (2)^1 * (3)^3 = 4 * 2 * 27 = 216.
Correct Answer:
B
— 48
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Q. In the expansion of (2x + 3)^4, what is the coefficient of x^2?
A.
108
B.
72
C.
36
D.
144
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Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
B
— 72
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Q. In the expansion of (2x + 3)^6, what is the coefficient of x^4?
A.
540
B.
720
C.
810
D.
900
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Solution
The coefficient of x^4 is C(6,4) * (2)^4 * (3)^2 = 15 * 16 * 9 = 2160.
Correct Answer:
B
— 720
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Q. In the expansion of (2x + 3y)^4, what is the coefficient of x^2y^2?
A.
108
B.
72
C.
36
D.
144
Show solution
Solution
The coefficient is C(4,2) * (2)^2 * (3)^2 = 6 * 4 * 9 = 216.
Correct Answer:
A
— 108
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Q. In the expansion of (2x + 5)^4, what is the coefficient of x^2?
A.
300
B.
600
C.
450
D.
500
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Solution
The coefficient of x^2 is C(4,2) * (2)^2 * (5)^2 = 6 * 4 * 25 = 600.
Correct Answer:
A
— 300
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Q. In the expansion of (2x - 3)^3, what is the coefficient of x?
A.
-9
B.
-18
C.
-27
D.
-6
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Solution
The coefficient of x is C(3,1) * (2)^1 * (-3)^2 = 3 * 2 * 9 = -54.
Correct Answer:
B
— -18
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^1?
A.
-15
B.
-30
C.
30
D.
15
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Solution
The coefficient of x^1 is C(5,1) * (2)^1 * (-3)^4 = 5 * 2 * 81 = 810.
Correct Answer:
B
— -30
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^2?
A.
-90
B.
-120
C.
-150
D.
-180
Show solution
Solution
The coefficient of x^2 is C(5,2) * (2)^2 * (-3)^3 = 10 * 4 * (-27) = -1080.
Correct Answer:
B
— -120
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^3?
A.
-540
B.
-720
C.
-960
D.
-1080
Show solution
Solution
The coefficient of x^3 is C(5,3) * (2)^3 * (-3)^2 = 10 * 8 * 9 = -720.
Correct Answer:
C
— -960
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Q. In the expansion of (2x - 3)^5, what is the coefficient of x^4?
A.
-90
B.
-120
C.
-150
D.
-180
Show solution
Solution
The coefficient of x^4 is C(5,4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.
Correct Answer:
B
— -120
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Q. In the expansion of (x + 1/x)^6, what is the coefficient of x^0?
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Solution
The coefficient of x^0 in (x + 1/x)^6 is given by 6C3 = 20.
Correct Answer:
C
— 20
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Q. In the expansion of (x + 1/x)^8, what is the coefficient of x^4?
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Solution
The coefficient of x^4 is C(8,4) = 70.
Correct Answer:
B
— 56
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Q. In the expansion of (x + 2)^5, what is the coefficient of x^3?
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Solution
The coefficient of x^3 is C(5,3) * (2)^2 = 10 * 4 = 40.
Correct Answer:
B
— 60
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Q. In the expansion of (x + 2)^6, what is the term containing x^4?
A.
240
B.
360
C.
720
D.
480
Show solution
Solution
The term containing x^4 is C(6,4) * (2)^2 * (x)^4 = 15 * 4 * x^4 = 60x^4.
Correct Answer:
C
— 720
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Q. In the expansion of (x + 2)^7, what is the term containing x^5?
A.
672
B.
6720
C.
67200
D.
672000
Show solution
Solution
The term containing x^5 is given by 7C5 * (2)^2 * (x)^5 = 21 * 4 * x^5 = 84x^5. Thus, the term is 84x^5.
Correct Answer:
B
— 6720
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Q. In the expansion of (x + 5)^6, what is the coefficient of x^3?
A.
150
B.
200
C.
250
D.
300
Show solution
Solution
The coefficient of x^3 is C(6, 3) * 5^3 = 20 * 125 = 250.
Correct Answer:
B
— 200
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Q. In the expansion of (x - 2)^6, what is the coefficient of x^4?
Show solution
Solution
The coefficient of x^4 is given by C(6,4) * (-2)^2 = 15 * 4 = 60.
Correct Answer:
C
— 90
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Q. In the expansion of (x - 2)^8, what is the coefficient of x^5?
A.
-2240
B.
-1280
C.
-1120
D.
-960
Show solution
Solution
The coefficient of x^5 is C(8,5) * (-2)^3 = 56 * (-8) = -448.
Correct Answer:
A
— -2240
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Q. In triangle ABC, if a = 7, b = 24, and c = 25, what is the area of the triangle?
A.
84
B.
96
C.
120
D.
144
Show solution
Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer:
A
— 84
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Showing 1831 to 1860 of 2847 (95 Pages)
Mathematics Syllabus (JEE Main) MCQ & Objective Questions
The Mathematics Syllabus for JEE Main is crucial for students aiming to excel in competitive exams. Understanding this syllabus not only helps in grasping key concepts but also enhances your ability to tackle objective questions effectively. Practicing MCQs and important questions from this syllabus is essential for solid exam preparation, ensuring you are well-equipped to score better in your exams.
What You Will Practise Here
Sets, Relations, and Functions
Complex Numbers and Quadratic Equations
Permutations and Combinations
Binomial Theorem
Sequences and Series
Limits and Derivatives
Statistics and Probability
Exam Relevance
The Mathematics Syllabus (JEE Main) is not only relevant for JEE but also appears in CBSE and State Board examinations. Students can expect a variety of question patterns, including direct MCQs, numerical problems, and conceptual questions. Mastery of this syllabus will prepare you for similar topics in NEET and other competitive exams, making it vital for your overall academic success.
Common Mistakes Students Make
Misinterpreting the questions, especially in word problems.
Overlooking the importance of units and dimensions in problems.
Confusing formulas related to sequences and series.
Neglecting to practice derivations, leading to errors in calculus.
Failing to apply the correct methods for solving probability questions.
FAQs
Question: What are the key topics in the Mathematics Syllabus for JEE Main? Answer: Key topics include Sets, Complex Numbers, Permutations, Binomial Theorem, and Calculus.
Question: How can I improve my performance in Mathematics MCQs? Answer: Regular practice of MCQs and understanding the underlying concepts are essential for improvement.
Now is the time to take charge of your exam preparation! Dive into solving practice MCQs and test your understanding of the Mathematics Syllabus (JEE Main). Your success is just a question away!
